基于马尔可夫链的无桩共享单车车辆投放规模分析

Analysis of dockless bike-sharing fleet size based on Markov chain

为动态优化无桩共享单车投放规模,加强规范化管理,采用马尔可夫随机过程的数学方法研究共享单车的投放问题.分析了无桩共享单车使用过程所具有的不可约、非周期和正常返等性质,为高效求解共享单车站点的稳态规模,通过构造转移概率随机素矩阵,使用向量迭代技术,提出“稀疏矩阵秩-修正算法”,并进一步讨论了稳态规模的依时间段动态求解问题.最后,结合数据对算法进行了验证与分析,得出共享单车马尔可夫链“极限状态(稳态)概率唯一存在且独立于初始概率分布”的结论.可用于解决无桩共享单车投放和调度中的无序问题.

In order to dynamically optimize the fleet size and strengthen standardized management of dockless bike-sharing,this paper uses the mathematical method of Markov stochastic process to study the problem of bike-sharing fleet size.Base on the analyze the use process of bike-sha-ring,proving it has three properties:irreducible,aperiodic and positive-recurrence,By construc-ting the transition probability random prime matrix and using the vector iterative technique,this paper proposes a"sparse matrix rank-one updating method"to solve the problem efficiently.Fur-thermore,It discuss the dynamic solution of bike-sharing steady-state fleet size according to the time period.At last,the algorithm is verified and analyzed by data,which is convinced that the algorithm can be used to solve the disordered deployment and rebalancing of dockless bike-sha-ring.It could draw a conclusion that the probability limit state(steady-state)of bike-sharing Markov chain only exists and is independent of the initial probability distribution.